If you used the standard 1 car length per 10 MPH, you were wrong in that the stopping distances are much different and you knew that.
What ever you are responsible, even just for going out the parked car could not be at fault.

The local government has no legal responsibility to keep roads free of ice and snow. The fact that you hit the other car proves you were driving too fast for conditions. That is a violation and gets you a ticket at a minimum.

Weather is not taken into consideration when involved in a collision. At least not as far as the insurance companies are concerned. You were driving too fast for conditions if you were involved in a weather-related accident. If the roads were too slippery, you shouldn't have been on them. Any time you get behind the wheel during inclement weather, you assume the risk, and therefore the responsibility, of having an accident.

A friend of mine made it to the top of a hill, but then the car wasn't making enough traction to keep going. So he put it in park, and set the parking brake. Went to step out, but realized he was sliding backwards down the hill. He hit a parked car. Guess who was at fault? My friend who had slid down the hill, while his vehicle was in park, is the "at fault" party of that accident. Under the circumstances, he wasn't ticketed with dangerous driving, or following too closely, etc.... but as the at-fault party he was responsible for all damages.

yes because the law or judge or whatever will say that you should have taken extra precautions while on the road in the winter, and whether you say you did or not, they will say that you still managed to hit the car, so they'll still say it's your fault.